biconncomp

Syntax

Description

bins = biconncomp(G)
returns the biconnected components
of graph G as bins. The bin numbers indicate which biconnected
component each edge in the graph belongs to. Each edge in G
belongs to a single biconnected component, whereas the nodes in G
can belong to more than one biconnected component. Two nodes belong to the same
biconnected component if removing any one node from the graph does not disconnect
them.

Group the graph nodes into bins based on which biconnected component(s) each node belongs to. Then, loop through each of the bins and extract a subgraph for each biconnected component. Label the nodes in each subgraph using their original node indices.

Input Arguments

G — Input graphgraph object

Input graph, specified as a graph object. Use graph to create an undirected graph object.

Example: G = graph(1,2)

Name-Value Pair Arguments

Specify optional
comma-separated pairs of Name,Value arguments. Name is
the argument name and Value is the corresponding value.
Name must appear inside single quotes (' '). You can
specify several name and value pair arguments in any order as
Name1,Value1,...,NameN,ValueN.

iC — Indices of cut verticesvector

More About

Biconnected Components

A biconnected component of a graph is a maximally biconnected
subgraph. A graph is biconnected if it does not contain any cut vertices.

Decomposing a graph into its biconnected components helps to measure how
well-connected the graph is. You can decompose any connected graph into a tree of
biconnected components, called the block-cut tree. The blocks
in the tree are attached at shared vertices, which are the cut vertices.

The illustration depicts:

(a) An undirected graph with 11 nodes.

(b) Five biconnected components of the graph, with the cut vertices of the
original graph colored for each component to which they belong.

(c) Block-cut tree of the graph, which contains a node for each
biconnected component (as large circles) and a node for each cut vertex (as
smaller multicolored circles). In the block-cut tree, an edge connects each
cut vertex to each component to which it belongs.

Cut Vertices

Also known as articulation points, cut
vertices are graph nodes whose removal increases the number of connected components.
In the previous illustration, the cut vertices are those nodes with more than one
color: nodes 4, 6, and 7.